The study of physical relationships between a physical stimuli acting upon an object is known to be helpful in better understanding the properties thereof. Stable systems exhibit linear behavior, follow the rules of superposition, and produce periodic output stimuli. For example, the behavior of magnetic objects subjected to magnetic fields is provided by an educational device for investigating and teaching about electromagnetic fields in U.S. Pat. No. 4,971,562. By using this device one can develop a better understanding of magnetic fields, electromagnetic forces and their interaction. It is also known to provide educational science toys as disclosed in U.S. Pat. No. 3,623,239. The device disclosed therein reveals a mechanical model of a cyclotron. Unfortunately, both of these devices provide predictable results based upon the input provided thereto.
Recently, it has been determined that by studying chaotic motion insight can be gained into systems that exhibit apparently random behavior. Systems that are nonlinear do not follow the rules of superposition and produce an output response that is not linearly proportional to its input stimuli. A system that exhibits chaotic behavior is a nonlinear system that is sensitive to initial conditions and whose output response transitions to an "exotic" steady state response that exhibits a quasi-random and aperiodic behavior. One such device that exhibits chaotic behavior is disclosed in U.S. Pat. No. 4,099,340. This device employs a series of rollers with projections that enclose a surface that supports a plurality of different size spheres. As the rollers rotate, their projections strike the spheres and generate observable random collisions. Although modifications may be made to the device to observe their effect, this device does not provide a means for analyzing a quantifiable or measured output.
In order to gain a proper understanding of chaos systems, such as the one above, systems examining random behavior have been revisited in light of recently developed chaos theories. Through measurement and observation, many of these systems exhibiting "random" behavior have been found to be deterministic, bounded and sensitive to initial conditions, which under the study of chaos, are defined as chaotic. To further the understanding of chaos, more measurement and observation of random systems is needed to categorize and develop mathematical models. Although some systems that exhibit chaotic behavior can be visualized by computer simulation of mathematical equations, these systems lack physical reality. Some chaotic systems exist in nature that have physical reality, but lack equivalent computer simulation due to their inherent complexity.
Based upon the foregoing, there is a need in the art for an apparatus which provides actual physical behavior that is measurable, provides reliable re-creation of results and is easy to modify with respect to altering the dynamics of the system.